prob_06_04_01 - Problem 6.4-1 Given: Consider two adjacent...

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Problem 6.4-1 Given: Consider two adjacent plane quadratic elements, as shown. Show that the shape functions provide interelement continuity of the field quanity along the boundary. Solution: Along the right edge of the left element: ξ 1 := N 2 1 4 1 ξ + () 1 η 1 4 1 ξ 2 1 η 1 4 1 ξ + 1 η 2 = N 2 η 2 2 η 2 = N 3 1 4 1 ξ + 1 η + 1 4 1 ξ + 1 η 2 1 4 1 ξ 2 1 η + = N 3 η 2 2 η 2 + = N 6 1 2 1 ξ + 1 η 2 = N 6 1 η 2 = let ϕ A ϕ 2 = ϕ B ϕ 3 = ϕ C ϕ 6 = ϕ N 2 ϕ A N 3 ϕ B + N 6 ϕ C + = η 2 η 2 ϕ A ηη 2 + 2 ϕ B + 1 η 2 ϕ C + = Along the left edge of the right element: ξ 1 := N 1 1 4 1 ξ 1 η 1 4 1 ξ 2 1 η 1 4 1 ξ 1 η 2 = N 1 η 2 2 η 2 = N 4 1 4 1 ξ 1 η + 1 4 1 ξ 2 1 η + 1 4 1 ξ 1 η 2 = N 4 η 2 2 η
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.

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